3x2 + 6x is ONE expression. A common factor is a factor that is COMMON to two (or more) expressions - not just one.
An alternative answer:
3x can be factored out of both of those.
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The greatest common factor of 12xy2 + 6x is 6x. The greatest common factor of 12 and 6 is 6, and the greatest common factor of xy2 and x is x. If you took 6x out of both factors, the end result would be 2y2+1
3x2 + 2x - 8 = 3x2 + 6x - 4x - 8 = 3x(x+2) - 4(x+2) = (3x-4)*(x+2)
(6x + 5)(6x + 5) or (6x + 5)2
x2 + 6x + 8 = (x + 4)(x + 2)
362+60x+25 (6x+5)(6x+5)